Geodesic
Schatten Class Operators in a Representation Space of Canonical Commutation Relations
Informatics and Automation, Modern problems of mathematical and theoretical physics, Tome 309 (2020), pp. 165-173.

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The Schatten classes $\mathfrak S_p$ of operators in a Hilbert space—a noncommutative analog of the classical $l_p$ spaces—play a significant role in recent studies on quantum information theory. In the present paper we give sufficient conditions for an operator to belong to $\mathfrak S_p$ in the case where the Hilbert space is the space of an irreducible representation of the canonical commutation relations. 
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     author = {A. S. Holevo},
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     url = {http://geodesic.mathdoc.fr/item/TRSPY_2020_309_a10/}
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A. S. Holevo. Schatten Class Operators in a Representation Space of Canonical Commutation Relations. Informatics and Automation, Modern problems of mathematical and theoretical physics, Tome 309 (2020), pp. 165-173. http://geodesic.mathdoc.fr/item/TRSPY_2020_309_a10/

[1] Agmon S., “On the eigenfunctions and on the eigenvalues of general elliptic boundary value problems”, Commun. Pure Appl. Math., 15 (1962), 119–147 | MR | Zbl

[2] Beigi S., “Sandwiched Rényi divergence satisfies data processing inequality”, J. Math. Phys., 54:12 (2013), 122202 | MR | Zbl

[3] De Palma G., Trevisan D., Giovannetti V., Ambrosio L., “Gaussian optimizers for entropic inequalities in quantum information”, J. Math. Phys., 59:8 (2018), 081101 | MR | Zbl

[4] Frank R.L., Lieb E.H., “Norms of quantum Gaussian multi-mode channels”, J. Math. Phys., 58:6 (2017), 062204 | MR | Zbl

[5] Gohberg I., Goldberg S., Krupnik N., Traces and determinants of linear operators, Oper. Theory: Adv. Appl., 116, Birkhäuser, Basel, 2000 | MR | Zbl

[6] I. C. Gohberg and M. G. Krein, Introduction to the Theory of Linear Nonselfadjoint Operators in Hilbert Space, Transl. Math. Monogr., 18, Am. Math. Soc., Providence, RI, 1969 | MR

[7] A. S. Holevo, Probabilistic and Statistical Aspects of Quantum Theory, 2nd ed., Edizioni della Normale, Pisa, 2011 | MR | Zbl

[8] A. S. Holevo, “Gaussian optimizers and the additivity problem in quantum information theory”, Russ. Math. Surv., 70:2 (2015), 331–367 | MR | Zbl

[9] J. R. Klauder and E. C. G. Sudarshan, Fundamentals of Quantum Optics, W.A. Benjamin, New York, 1968 | MR

[10] V. I. Paraska, “On the asymptotics of eigenvalues and singular numbers of linear smoothing operators”, Am. Math. Soc. Transl., Ser. 2, 79 (1969), 87–95 | MR | Zbl | Zbl